First Edition (version 1.0) published online on 08 May 2009 This file shall be a good reference to vector identities and their proofs. The first main purpose of this file is to show that the the time duration for the second round of bad deed can mature faster than the time duration for the first round of bad deed. This is due to lower trust and credit in the second round of bad deed after the first round of bad deed. The second main purpose is to encourage good people to revenge rightly by... Topics: Vector identity, nabla operator, how to be good people, action towards bad people.